Sparse Kalman filter

In this work, a sparse Kalman filter (SKF) exploring the signal sparse property is developed to track unknown time-varying signals. To derive SKF, the measurement update in KF is reformulated into a convex optimization problem first, and then a regularization term ℓ₁-norm on parameters of interest is introduced to yield sparse estimates. Coupled the reformulated measurement update with prediction step in KF, the SKF is achieved. The SKF method can be straightforwardly implemented in the standard KF framework, in which it does not require pseudo measurements. Numerical studies demonstrate the superior performance of SKF compared to other reconstruction schemes.